When workpieces are machined by a robot, a complex machine tool or a machining center, it is necessary to carry out, among other things, switching operations related to movement. Such switching operations can include, for instance, closing or opening an electrode holder used in spot welding, switching the welding current on and off when an electric arc or laser is used in contour welding, or connecting or disconnecting the bulk current of a tool such as a glue gun, etc. for bonding and sealing work. These switching operations are carried out at certain positions on the trajectory path completed by the tool. The term "position" refers not only to the spatial point where a tool is situated, but also to the alignment of the tool at this spatial point. In the case of a robot, this alignment is usually referred to as the "orientation" thereof.
When the trajectory for the tool of the robot, of the machine tool, or of some other numerically controlled system is specified exactly by coordinate values, for example by Cartesian coordinates, the position where the switching operation is supposed to be initiated can also be specified in these coordinates. However, it is cumbersome to enter coordinate values as setpoint values, since several values are always required. A far more serious disadvantage of this method for triggering switching operations lies, however, in that numerically controlled systems are provided with several possibilities for generating a path between two points. In addition to the already mentioned coordinate-specific movement along a trajectory path, described as continuous-path (CP) movement, there could be, for example, a point-to-point (PTP) and/or a looping (UE) movement. In the case of point-to-point movement, the axes of the numerically controlled system are travelled in a way which allows the target point to be approached with the smallest angle change for each axis. Therefore, the path between two points of a point-to-point movement along a path completed by the tool is, first of all, not necessarily a straight line, and secondly, is not known in coordinates. In this case as well, no switching operation can be initiated in response to a specific coordinate value. The same applies to looping movements along a path, in which case individual motion blocks are interconnected by a looping contour in such a way that the movements of the tool from one motion block to the other blend continuously into one another.
Another difficulty in establishing a defined switching point lies in that the actual values of the tool position of the numerically controlled system differ by a following error value from the setpoint values calculated by the numerical control. This following error value increases as the tool path feedrate increases.